Originally posted by tomtom232
A line of 100 airline passengers is waiting to board a plane. They each hold a ticket to one of the 100 seats on that flight. Unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. All of the other passengers are quite normal, and will go to their proper seat unless it is already ...[text shortened]... in their proper seat?
Will the probability change if you add another person? Why or why not?
At first I was thinking 1/100, but then I realized that only two seats on the plane really matter, seat 1 and seat 100. For every person that is displaced (and it doesn't matter how many), each displaced person has an equal probability of sitting in either seat 1 or seat 100.
If anyone sits in seat 1, everyone else will sit in the correct seat. [100%]
On the other hand, if anyone sits in seat 100, the last person can't sit in their own seat [0%].
Therefore, I would think that the average of these, 50%, is the probability of the last person sitting in their own seat.